Python program to print the octal value of the numbers from 1 to N

Given a number N, the task is to write a Python program to print the octal value of the numbers from 1 to N.

Examples:

Approach:

• We will take the value of N as input.
• Then, we will run the for loop from 1 to N+1 and traverse each "i" through oct() function.
• Print each octal value.

Note: The oct() function is one of the built-in methods in Python3. The oct() method takes an integer and returns its octal representation in a string format. 

Below are the implementations based on the above approach:

Input: 3
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Input: 11
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Time complexity: O(n), where n is the input argument to the function. The time complexity is linear as the for loop traverses the range from 1 to N.

Space complexity: O(1), as the function only uses a constant amount of extra space to store the temporary variables i and the octal representation of i.

Approach: Decimal to Octal Conversion using repeated division by 8

1. Define a function named decimal_to_octal that takes a decimal number as an argument and converts it to its octal representation using repeated division by 8 and concatenating the remainders.
2. In the decimal_to_octal function, initialize a variable octal_num to 0 and a variable i to 1.
3. Using a while loop, repeatedly divide the decimal number by 8 and compute the remainder.
4. Divide the decimal number by 8 using the floor division operator // and update the value of the decimal number.
5. Multiply the remainder by i and add it to the octal_num.
6. Multiply i by 10 to shift the position of the next digit to be added to the left.
7. After the loop finishes, return the octal_num as the octal representation of the original decimal number.
8. In the main program, take user input for a number n.
9. Use a for loop to iterate over the numbers from 1 to n inclusive.
10. For each number i in the loop, call the decimal_to_octal function on i and print the resulting octal value.
11. The final output will be the octal representation of all the numbers from 1 to n.

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The time complexity of this program is O(n log n), where n is the input number, The auxiliary space used by this program is O(1).

List Comprehension with Join method

The idea is to create a list comprehension that generates octal values for each number from 1 to N and print the octal values on separate lines using the join() method.

Steps:

1. Initialize a variable N to the user input.
2. Generate a list of octal values using a list comprehension that iterates over the range from 1 to N and applies the built-in oct() function to each number.
3. Join the octal values using the join() method and print them on separate lines.

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Time Complexity: O(N)
Auxiliary Space: O(N), used to store the list of octal values